i may catch some flak for this, but if i had no equipment and i had not advanced to one arm pushups and pistols i would do 15 mins of slow deliberate technically sound burpees. Not as many as i can in the time allotted, but a slow practice holding each step of the movement, roughly 3 to 5 per minute. it is a good overall body movement, requires a sufficient balance of strength and flexibility conditioning, can be performed in small spaces and is easy to perform.
I'd spend the 15 minutes doing all kinds of movements from Original Strength. You get strength, mobility and a little bit of cardio when you play hard. No equipment required and only limited by your own imagination.
PS: That is actually pretty much what I am actually doing at the moment.
Due to the time issue personally I would pick one exercise and one stretch and use that time to perfect both. Keep the exercises basic and work on different forms and cadences. Ex.. Assign one day to be push up day. Then you pick and chose whether you want to work on explosiveness, time under tension (slow), different forms such as diamond, wide, dragon walks (spider mans), Hindu, etc. then work on stretching an area from either that workout or the previous day. This will allow you to keep track of your progress and will only take a few minutes to plan out a month or two.
Body weight exercises -
Bent over shoulder press
Neck "around the world"
Shrimp and pistol squats
I quickly scanned thru this but might have missed some of your ideas.. so forgive me it anything I add is repeating what has been posted.
I want to first ask what is your goal? I get questions often about programming and what I would do if this or if that....however rarely do they start with what they actually want to accomplish. So, my first answer is often IT DEPENDS. If you have only 15 mins a day and you want to just move and keep up your general health and fitness then my answer would be very different than if you said I want to continue to gain strength but only have 15 mins a day.
So if your goal is to increase your strength I would recommend doing OAPU progressions and pistols or SLDL as they have great carryover and do not take very long to do. I would also do pull up as GTG, if you are near a bar to do so. Otherwise you could do pullups and pistols or SLDL and do your OAPU progressions in a GTG through out the day.
My next question would be what is your job? This would determine what other skills could be mixed into your day to compliment your 15 mins of training daily.